Understanding vector elds resulting from large scientific simulations is an important and often dicult task. Integral curves, curves that are tangential to a vector field at each point, are a powerful visualization method in this context. Application of integral curve-based visualization to very large vector field data represents a significant challenge due to the non-local and data-dependent nature of integral curve computation, and requires careful balancing of computational demands placed on I/O, memory, communication, and processors. In this chapter we review several dierent parallelization approaches based on established parallelization paradigms (across particles, and data blocks) and present advanced techniques for achieving scalable, parallel performance on very large data sets.